# Network Topology Inference from Smooth Signals Under Partial Observability

arXiv: https://arxiv.org/abs/2410.05707 · HTML: https://mlsanity.com/paper/2410.05707/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 72 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 26 of 26)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Robustness of Graph Neural Networks at Scale](https://mlsanity.com/paper/2110.14038/) (2021)
- [Graph Representation Learning: A Survey](https://mlsanity.com/paper/1909.00958/) (2019)
- [Multi-Modal Knowledge Graph Construction and Application: A Survey](https://mlsanity.com/paper/2202.05786/) (2022)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [A Comprehensive Survey on Community Detection with Deep Learning](https://mlsanity.com/paper/2105.12584/) (2021)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [Shifu2: A Network Representation Learning Based Model for Advisor-advisee Relationship Mining](https://mlsanity.com/paper/2008.07097/) (2020)
- [Learning Graphs from Smooth and Graph-Stationary Signals with Hidden Variables](https://mlsanity.com/paper/2111.05588/) (2021)
- [Online Discriminative Graph Learning from Multi-Class Smooth Signals](https://mlsanity.com/paper/2101.00184/) (2021)
- [Joint Network Topology Inference in the Presence of Hidden Nodes](https://mlsanity.com/paper/2306.17364/) (2023)
- [Grid-Graph Signal Processing (Grid-GSP): A Graph Signal Processing Framework for the Power Grid](https://mlsanity.com/paper/2103.06068/) (2021)
- [Kernel-Based Structural Equation Models for Topology Identification of Directed Networks](https://mlsanity.com/paper/1605.03122/) (2016)
- [SILVar: Single Index Latent Variable Models](https://mlsanity.com/paper/1705.03536/) (2017)
- [Physics Informed Topology Learning in Networks of Linear Dynamical Systems](https://mlsanity.com/paper/1809.10535/) (2018)
- [Web of Scholars: A Scholar Knowledge Graph](https://mlsanity.com/paper/2202.11311/) (2022)
- [Statistical Inference for H"usler-Reiss Graphical Models Through Matrix Completions](https://mlsanity.com/paper/2210.14292/) (2022)
- [Topology Identification under Spatially Correlated Noise](https://mlsanity.com/paper/2012.04175/) (2020)
- [An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability](https://mlsanity.com/paper/2203.15500/) (2022)
- [City-wide Analysis of Electronic Health Records Reveals Gender and Age Biases in the Administration of Known Drug-Drug Interactions](https://mlsanity.com/paper/1803.03571/) (2018)
- [Topology Inference for Network Systems: Causality Perspective and Non-asymptotic Performance](https://mlsanity.com/paper/2106.01031/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning Graph from Smooth Signals under Partial Observation: A Robustness Analysis](https://mlsanity.com/paper/2509.14887/) (2025)
- [Learning Time-Varying Graphs from Incomplete Graph Signals](https://mlsanity.com/paper/2510.17903/) (2025)

## Abstract (arXiv)

Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered hidden nodes and proposed various optimization frameworks, existing methods often lack the practical efficiency needed for large-scale networks or fail to provide theoretical convergence guarantees. In this paper, we address the problem of inferring network topologies from smooth signals with partially observed nodes. We propose a first-order algorithmic framework that includes two variants: one based on column sparsity regularization and the other on a low-rank constraint. We establish theoretical convergence guarantees and demonstrate the linear convergence rate of our algorithms. Extensive experiments on both synthetic and real-world data show that our results align with theoretical predictions, exhibiting not only linear convergence but also superior speed compared to existing methods. To the best of our knowledge, this is the first work to propose a first-order algorithmic framework for inferring network structures from smooth signals under partial observability, offering both guaranteed linear convergence and practical effectiveness for large-scale networks.